Random Walks between Leaves of Random Networks

Abstract: We consider random walks that start and are absorbed on the leaves of random networks and study the length of such walks. For the networks we investigate, Erdos-Renyi random graphs and Barabasi-Albert scale free networks, these walks are not transient and we consider various approaches to computing the probability of a given length walk.One approach is to label nodes according to both their total degree and the number of links connected to leaf nodes, and as a byproduct we compute the probability of a random node of a scale free network having such a label.